Multifidelity Bayesian Optimisation with Continuous Approximations
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:17991808, 2017.
Abstract
Bandit methods for blackbox optimisation, such as Bayesian optimisation, are used in a variety of applications including hyperparameter tuning and experiment design. Recently, multifidelity methods have garnered considerable attention since function evaluations have become increasingly expensive in such applications. Multifidelity methods use cheap approximations to the function of interest to speed up the overall optimisation process. However, most multifidelity methods assume only a finite number of approximations. On the other hand, in many practical applications, a continuous spectrum of approximations might be available. For instance, when tuning an expensive neural network, one might choose to approximate the cross validation performance using less data $N$ and/or few training iterations $T$. Here, the approximations are best viewed as arising out of a continuous two dimensional space $(N,T)$. In this work, we develop a Bayesian optimisation method, BOCA, for this setting. We characterise its theoretical properties and show that it achieves better regret than than strategies which ignore the approximations. BOCA outperforms several other baselines in synthetic and real experiments.
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